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Centroid of Integral Area?

  1. Mar 29, 2015 #1
    If I have an integrated area such as the blue area in the link below, what function can be written to find the location on the x axis where half of the area is one side and half is on the other or more specifically a function that determines the x-axis location of the centroid?

    http://images.encydia.com/thumb/f/f9/Areabetweentwographs.svg/180px-Areabetweentwographs.svg.png [Broken]
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Mar 29, 2015 #2

    SteamKing

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    It depends on what exactly you want to find. The centroid of an area is not necessarily the same as the line which divides a region into two equal areas.

    The location of the x coordinate of the centroid is the first moment of area about the y-axis divided by the area, or

    x-bar = [ ∫ x * f(x) dx ] / [ ∫ f(x) dx ]
     
    Last edited by a moderator: May 7, 2017
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